On a conjecture of quintas and arc-traceability in upset tournaments

• Autorzy: Arthur H. Busch , Michael S. Jacobson , K. Brooks Reid
• Języki publikacji: EN

Abstrakty

EN

A digraph D = (V,A) is arc-traceable if for each arc xy in A, xy lies on a directed path containing all the vertices of V, i.e., hamiltonian path. We prove a conjecture of Quintas [7]: if D is arc-traceable, then the condensation of D is a directed path. We show that the converse of this conjecture is false by providing an example of an upset tournament which is not arc-traceable. We then give a characterization for upset tournaments in terms of their score sequences, characterize which arcs of an upset tournament lie on a hamiltonian path, and deduce a characterization of arc-traceable upset tournaments.

Słowa kluczowe

EN

tournament; upset tournament; traceable

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 3
• Strony: 225-239

Daty

wydano

2005

otrzymano

2004-03-24

poprawiono

2005-01-13

Twórcy

autor

Arthur H. Busch

• Department of Mathematics, University of Colorado at Denver, Denver, CO 80217, USA

autor

Michael S. Jacobson

• Department of Mathematics, University of Colorado at Denver, Denver, CO 80217, USA

autor

K. Brooks Reid

• Department of Mathematics, California State University San Marcos, San Marcos, CA 92096, USA

Bibliografia

• [1] K.T. Balińska, M.L. Gargano and L.V. Quintas, An edge partition problem concerning Hamilton paths, Congr. Numer. 152 (2001) 45-54.
• [2] K.T. Balińska, K.T. Zwierzyński, M.L. Gargano and L.V. Quintas, Graphs with non-traceable edges, Computer Science Center Report No. 485, The Technical University of Poznań (2002).
• [3] K.T. Balińska, K.T. Zwierzyński, M.L. Gargano and L.V. Quintas, Extremal size problems for graphs with non-traceable edges, Congr. Numer. 162 (2003) 59-64.
• [4] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer-Verlag, Berlin, 2001).
• [5] R.A. Brualdi and Q. Li, The interchange graph of tournaments with the same score vector, in: Progress in graph theory, Proceedings of the conference on combinatorics held at the University of Waterloo, J.A. Bondy and U.S.R. Murty editors (Academic Press, Toronto, 1982), 129-151.
• [6] M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).
• [7] L.V. Quintas, private communication, (2001).
• [8] L. Rédei, Ein Kombinatorischer Satz, Acta Litt. Szeged. 7 (1934) 39-43.
• [9] K.B. Reid, Tournaments, in: The Handbook of Graph Theory, Jonathan Gross and Jay Yellen editors (CRC Press, Boca Raton, 2004).

Identyfikatory

DOI

10.7151/dmgt.1287